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Free Grade 3 Magnitude of a Vector Flashcards

Free Grade 3 flashcards for Magnitude of a Vector: 12 real questions with a full answer key and worked solutions. A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).

Price

Free

Difficulty

Foundation

Estimated time

30 min

Total marks

24

Learning objectives

Every objective is checkable, and each one maps to an activity and an assessment.

  • UnderstandExplain magnitude of a vector

    Explain magnitude of a vector accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • ApplyCalculate magnitude of a vector

    Calculate magnitude of a vector accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • AnalyseCompare magnitude of a vector

    Compare magnitude of a vector accurately in a familiar context.

    Assessed by: Exit ticket of four short items

  • EvaluateJustify magnitude of a vector

    Justify magnitude of a vector accurately in a familiar context.

    Assessed by: Exit ticket of four short items

Prerequisites

Close these gaps first — each has its own free lesson, worksheet and quiz.

Scalar Multiples
Adding Vectors
Calculus

How Magnitude of a Vector works

A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).

Key wordsvectormagnitudecomponentscalar

12 practice questions

Easy to hard, 24 marks in total. Try them first, then open the answers.

  1. 1.a = (-1, -5), b = (-4, 3). Find a + 2b.[1]
  2. 2.a = (-4, 3), b = (3, 4). Find a + 2b.[1]
  3. 3.a = (1, -5), b = (-1, 0). Find a + 4b.[1]
  4. 4.a = (-3, 0), b = (-1, -4). Find a + 2b.[1]
  5. 5.a = (-6, 6), b = (1, -3). Find a + 4b.[2]
  6. 6.a = (2, 3), b = (-4, 4). Find a + 2b.[2]
  7. 7.a = (1, -3), b = (-1, 0). Find a + 2b.[2]
  8. 8.a = (-5, 2), b = (0, -4). Find a + 3b.[2]
  9. 9.Find the magnitude of (6, 5) to 2 d.p.[3]
  10. 10.Find the magnitude of (-1, 0) to 2 d.p.[3]
  11. 11.Find the magnitude of (-5, -6) to 2 d.p.[3]
  12. 12.Find the magnitude of (4, -5) to 2 d.p.[3]
Show answers and working

  1. 1. (-9, 1)

    2b = (-8, 6). Add components: (-1 + -8, -5 + 6).

  2. 2. (2, 11)

    2b = (6, 8). Add components: (-4 + 6, 3 + 8).

  3. 3. (-3, -5)

    4b = (-4, 0). Add components: (1 + -4, -5 + 0).

  4. 4. (-5, -8)

    2b = (-2, -8). Add components: (-3 + -2, 0 + -8).

  5. 5. (-2, -6)

    4b = (4, -12). Add components: (-6 + 4, 6 + -12).

  6. 6. (-6, 11)

    2b = (-8, 8). Add components: (2 + -8, 3 + 8).

  7. 7. (-1, -3)

    2b = (-2, 0). Add components: (1 + -2, -3 + 0).

  8. 8. (-5, -10)

    3b = (0, -12). Add components: (-5 + 0, 2 + -12).

  9. 9. 7.81

    |v| = √(x² + y²) = √(36 + 25). = 7.81.

  10. 10. 1

    |v| = √(x² + y²) = √(1 + 0). = 1.

  11. 11. 7.81

    |v| = √(x² + y²) = √(25 + 36). = 7.81.

  12. 12. 6.4

    |v| = √(x² + y²) = √(16 + 25). = 6.4.

Worked examples

Easy example

a = (-4, 4), b = (6, 2). Find a + 4b.

  1. 4b = (24, 8).
  2. Add components: (-4 + 24, 4 + 8).
  3. Answer: (20, 12)
Medium example

a = (-2, -6), b = (1, -4). Find a + 4b.

  1. 4b = (4, -16).
  2. Add components: (-2 + 4, -6 + -16).
  3. Answer: (2, -22)
Hard example

Find the magnitude of (3, -5) to 2 d.p.

  1. |v| = √(x² + y²) = √(9 + 25).
  2. = 5.83.
  3. Answer: 5.83

Interactive practice

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Common mistakes

What learners typically get wrong, and how to fix it.

  • Adds x of one vector to y of the other.

    Correction: Add x with x, y with y.

  • Forgets that a negative component means the opposite direction.

    Correction: Draw the vector to check.

Teacher tips

  • · Draw vectors on squared paper end to end.

Parent tips

  • · Give directions as '3 steps right, 2 steps up'.

Real-life applications

  • · Navigation, forces in physics, game movement.

Assessment objectives

How mastery is evidenced, and which standards it maps to.

NATIONAL-CURRICULUM NAT-919.1 — Mapped statement covering Magnitude of a Vector.IB IB-624.2 — Mapped statement covering Magnitude of a Vector.

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Goes deeper

The entities below this one, each with the same complete free resource set.

Introducing Magnitude of a Vector
Working with Magnitude of a Vector
Magnitude of a Vector in Context

Sibling concepts

Vector Notation
Adding Vectors
Scalar Multiples

Related concepts

Lateral links, including across subjects.

Vector Notation
Adding Vectors
Scalar Multiples
Vector Geometry

Next topics

Vector Geometry

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Frequently asked

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What should a learner already know before this?
Start with Scalar Multiples, Adding Vectors, Calculus. Each one has its own free lesson, worksheet and quiz.
How is the flashcards sequenced?
Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
What comes next after Magnitude of a Vector?
Move on to Vector Geometry, which build directly on this idea.

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